08-Find Whole Given Part and Percent
In previous lessons, we’ve learned how to find the percent of a number; say, if you scored 92% on a test with 50 questions, how many questions did you get correct? You end up multiplying the two like so:
But what if the question seems a little backwards. You got 36 questions correct on a test. This was a 90%. How many question were on the test? So you’ve been given the percentage, and the part, and have been asked to find the whole. To figure this out, you are basically setting up an equation:
The whole becomes an unknown, which we make a variable. You then set up the multiplication the same way you did for percent of a number. Convert the percentage to a decimal, and multiple. Your equation would then look like this:
.9a = 36
From there, simply remember our two key words for solving equations: OPPOSITE OPERATIONS, and you’re golden. The opposite of multiply is divide, so we’ll solve the equation like so:
Now to finish solving for our whole, the variable, we do need to divide with a decimal. This takes us back to our lesson on the frog and the dog. If you need a refresher on decimal division, click here. Our example problem would look like this:
Thus our unknown is 40. There are 40 question on the test. 90% of 40 = 36.